Light

Properties of light are fundamental

Almost everything we know about the universe outside our solar system comes from interpreting the light from distant objects.

Light is weirder than you think

Here are some slides I’ve used for introductory astronomy as a guide to some properties of light. The math here might be useful in figuring out your own stories involving light.

Radiation: Two different kinds

Something that “radiates”, or spreads out in “rays”

High speed particles (eg. high speed neutrons ejected from a disintegrating atomic nucleus)

Electromagnetic radiation:

Towards shorter “wavelength” and higher energy:

Visible light, Ultraviolet light, X-Rays, Gamma-Rays

Towards longer “wavelength” and lower energy:

Visible light, Infrared radiation, microwaves, radio waves

Properties of Light

Light has both wave and particle properties

Travels like a wave

Interacts with matter like a particle: “photon”

Full explanation involves quantum mechanics

For most cases we can just choose the right “model” from the above two choices

Photons, unlike particles in other kinds of “radiation,” are particles of “pure energy”

Light is an electromagnetic wave

Changing electric fields generates magnetic fields

Changing magnetic fields generates electric fields

Can set up a cycle where one field causes the other:

The E and B fields oscillate in strength, and the disturbance moves forward.

To describe the wave you need to specify

Direction it is moving

Strength of the fields (its intensity)

Frequency or Wavelength of the oscillation (u and l are inversely related)

Orientation of the electric E field: up or sideways (polarization)

You do not need to specify its speed

In a vacuum all lightwaves move at the same speed c = 3´10⁸ m/s

The Electromagnetic Spectrum

Radio waves

Microwaves

Infrared

Visible

Ultra-violet

X-Rays

Gamma rays

Relationship between Energy and Wavelength of Light

Short wavelength Þ High energy photons

Long wavelength Þ Low energy photons

Intensity µ total energy (per area per second)

µ (# of photons per area per second)
´ (energy per photon)

Example with falling rain:

Amount of rain µ (# of raindrops) ´ (volume per drop)

Why is energy per photon so important?

Real life example: Ultra-Violet light hitting your skin

Threshold for chemical damage set by energy (wavelength) of photons

Below threshold (long wavelengths) energy too weak to cause chemical changes

Above threshold (short wavelength) energy photons can break apart DNA molecules

Number of molecules damaged = number of photons above threshold

Very unlikely two photons can hit exactly together to cause damage

Numerical Relationship between
wavelength and photon energy

Inverse relationship: Smaller l means more energetic

c = speed of light = 3.00 ´ 10⁸ m/s

h = Planck’s constant = 6.63 ´ 10^-34 joule/s

Note: Joule is a unit of energy 1 Joule/second = 1 Watt

Energy of a single photon of 0.5 mm visible light?

Seems very small, but this is roughly the energy it takes to chemically modify a single molecule.

Photons from a 100 W lightbulb (assuming all 100W goes into light?)

Temperature and Heat

Thermal energy is “kinetic energy” of moving atoms and molecules

Hot material energy has more energy available which can be used for

Chemical reactions

Nuclear reactions (at very high temperature)

Escape of gasses from planetary atmospheres

Creation of light

Collision bumps electron up to higher energy orbit

It emits extra energy as light when it drops back down to lower energy orbit

(Reverse can happen in absorption of light)

Temperature Scales

Want temperature scale where energy is proportional to T

Celsius scale is “arbitrary” (Fahrenheit even more so)

0^o C = freezing point of water

100^o C = boiling point of water

By experiment, available energy = 0 at “Absolute Zero” = –273^oC (-459.7^oF)

Define “Kelvin” scale with same step size as Celsius, but 0K = -273^oC = Absolute Zero

Use Kelvin Scale for most of work in this course

Available energy is proportional to T, making equations simple (really! OK, simpler)

273K = freezing point of water

373K = boiling point of water

300K approximately room temperature

Planck “Black Body Radiation”

Hot objects glow (emit light)

Heat (and collisions) in material causes electrons to jump to high energy orbits

As electrons drop back down, some of energy is emitted as light.

Reason for name “Black Body Radiation”

In a “solid” body the close packing of the atoms means than the electron orbits are complicated, and virtually all energy orbits are allowed. So all wavelengths of light can be emitted or absorbed. (In a gas with isolated atoms, only certain orbits are permitted so only certain wavelengths can be absorbed or emitted.)

A black material is one which readily absorbs all wavelengths of light. These turn out to be the same materials which also readily emit all wavelengths when hot.

The hotter the material the more energy it emits as light

As you heat up a filament or branding iron, it glows brighter and brighter

The hotter the material the more readily it emits high energy (blue) photons

As you heat up a filament or branding iron, it first glows dull red, then bright red, then orange, then if you continue, yellow, and eventually blue

Planck and other Formulae

Planck formula gives intensity of light at each wavelength

It is complicated. We’ll use two simpler formulae which can be derived from it.

Wien’s law tells us what wavelength has maximum intensity

Stefan-Boltzmann law tells us total radiated energy per unit area

Example of Wien’s law

What is wavelength at which you glow?

Room T = 300 K so

This wavelength is about 20 times longer than what your eye can see. Camera in class operated at 7-14 μm.

What is temperature of the sun – which has maximum intensity at roughly 0.5 mm?

Kirchoff’s laws

Hot solids emit continuous spectra

Hot gasses try to do this, but can only emit discrete wavelengths

Cold gasses try to absorb these same discrete wavelengths

Atoms – Electron Configuration

Molecules: Multiple atoms sharing/exchanging electrons (H₂O, CH₄)

Ions:          Single atoms where one or more electrons have escaped (H⁺⁾

Binding energy:   Energy needed to let electron escape

Permitted “orbits” or energy levels

By rules of quantum mechanics, only certain “orbits” are allowed

Ground State: Atom with electron in lowest energy orbit

Excited State: Atom with at least one atom in a higher energy orbit

Transition:    As electron jumps from one energy level orbit to another,
atom must release/absorb energy different, usually in form of light.

Because only certain orbits are allowed, only certain energy jumps are allowed, and atoms can absorb or emit only certain energies (wavelengths) of light.

In complicated molecules or “solids” many orbits and transitions are allowed

Can use energy levels to “fingerprint” elements and estimate temperatures.

Hydrogen Lines

Energy absorbed/emitted depends on upper and lower levels

Higher energy levels are close together

Above a certain energy, electron can escape (ionization)

Series of lines named for bottom level

To get absorption, lower level must be occupied

Depends upon temperature of atoms

To get emission, upper level must be occupied

Can get down-ward cascade through many levels


	Properties of light are fundamental

	Almost everything we know about the universe outside our solar system comes from interpreting the light from distant objects.

	Light is weirder than you think

	Here are some slides I’ve used for introductory astronomy as a guide to some properties of light. The math here might be useful in figuring out your own stories involving light.


Something that “radiates”, or spreads out in “rays”

High speed particles (eg. high speed neutrons ejected from a disintegrating atomic nucleus)

Electromagnetic radiation:
	Towards shorter “wavelength” and higher energy:
		Visible light, Ultraviolet light, X-Rays, Gamma-Rays
	Towards longer “wavelength” and lower energy:
		Visible light, Infrared radiation, microwaves, radio waves


Light has both wave and particle properties
	Travels like a wave
	Interacts with matter like a particle: “photon”

		Full explanation involves quantum mechanics
		For most cases we can just choose the right “model” from the above two choices
		Photons, unlike particles in other kinds of “radiation,” are particles of “pure energy”


	Changing electric fields generates magnetic fields
	Changing magnetic fields generates electric fields
	Can set up a cycle where one field causes the other:
		The E and B fields oscillate in strength, and the disturbance moves forward.







	To describe the wave you need to specify
		Direction it is moving
		Strength of the fields (its intensity)
		Frequency or Wavelength of the oscillation (u and l are inversely related)
		Orientation of the electric E field: up or sideways (polarization)
	You do not need to specify its speed
		In a vacuum all lightwaves move at the same speed c = 3´10⁸ m/s


	Radio waves
	Microwaves
	Infrared
	Visible
	Ultra-violet
	X-Rays
	Gamma rays


	Short wavelength Þ High energy photons
	Long wavelength Þ Low energy photons

	Intensity µ total energy (per area per second) µ (# of photons per area per second) ´ (energy per photon)

	Example with falling rain:
		Amount of rain µ (# of raindrops) ´ (volume per drop)


Real life example: Ultra-Violet light hitting your skin
	Threshold for chemical damage set by energy (wavelength) of photons
		Below threshold (long wavelengths) energy too weak to cause chemical changes
		Above threshold (short wavelength) energy photons can break apart DNA molecules
	Number of molecules damaged = number of photons above threshold
	Very unlikely two photons can hit exactly together to cause damage


Inverse relationship: Smaller l means more energetic
	c = speed of light = 3.00 ´ 10⁸ m/s
	h = Planck’s constant = 6.63 ´ 10^-34 joule/s
		Note: Joule is a unit of energy 1 Joule/second = 1 Watt
Energy of a single photon of 0.5 mm visible light?


	Seems very small, but this is roughly the energy it takes to chemically modify a single molecule.
Photons from a 100 W lightbulb (assuming all 100W goes into light?)



Thermal energy is “kinetic energy” of moving atoms and molecules
	Hot material energy has more energy available which can be used for
		Chemical reactions
		Nuclear reactions (at very high temperature)
		Escape of gasses from planetary atmospheres
		Creation of light
			Collision bumps electron up to higher energy orbit
			It emits extra energy as light when it drops back down to lower energy orbit
			(Reverse can happen in absorption of light)



Want temperature scale where energy is proportional to T
	Celsius scale is “arbitrary” (Fahrenheit even more so)
		0^o C = freezing point of water
		100^o C = boiling point of water
	By experiment, available energy = 0 at “Absolute Zero” = –273^oC (-459.7^oF)
	Define “Kelvin” scale with same step size as Celsius, but 0K = -273^oC = Absolute Zero

Use Kelvin Scale for most of work in this course
	Available energy is proportional to T, making equations simple (really! OK, simpler)
	273K = freezing point of water
	373K = boiling point of water
	300K approximately room temperature



	Hot objects glow (emit light)
		Heat (and collisions) in material causes electrons to jump to high energy orbits
		As electrons drop back down, some of energy is emitted as light.

	Reason for name “Black Body Radiation”
		In a “solid” body the close packing of the atoms means than the electron orbits are complicated, and virtually all energy orbits are allowed. So all wavelengths of light can be emitted or absorbed. (In a gas with isolated atoms, only certain orbits are permitted so only certain wavelengths can be absorbed or emitted.)

		A black material is one which readily absorbs all wavelengths of light. These turn out to be the same materials which also readily emit all wavelengths when hot.

	The hotter the material the more energy it emits as light
		As you heat up a filament or branding iron, it glows brighter and brighter

	The hotter the material the more readily it emits high energy (blue) photons
		As you heat up a filament or branding iron, it first glows dull red, then bright red, then orange, then if you continue, yellow, and eventually blue



	Planck formula gives intensity of light at each wavelength
		It is complicated. We’ll use two simpler formulae which can be derived from it.

	Wien’s law tells us what wavelength has maximum intensity



	Stefan-Boltzmann law tells us total radiated energy per unit area



	What is wavelength at which you glow?
		Room T = 300 K so



		This wavelength is about 20 times longer than what your eye can see. Camera in class operated at 7-14 μm.

	What is temperature of the sun – which has maximum intensity at roughly 0.5 mm?



	Hot solids emit continuous spectra

	Hot gasses try to do this, but can only emit discrete wavelengths

	Cold gasses try to absorb these same discrete wavelengths



	Molecules: Multiple atoms sharing/exchanging electrons (H₂O, CH₄)

	Ions: Single atoms where one or more electrons have escaped (H⁺⁾

	Binding energy: Energy needed to let electron escape

	Permitted “orbits” or energy levels
		By rules of quantum mechanics, only certain “orbits” are allowed
		Ground State: Atom with electron in lowest energy orbit
		Excited State: Atom with at least one atom in a higher energy orbit
		Transition: As electron jumps from one energy level orbit to another, atom must release/absorb energy different, usually in form of light.
	Because only certain orbits are allowed, only certain energy jumps are allowed, and atoms can absorb or emit only certain energies (wavelengths) of light.
	In complicated molecules or “solids” many orbits and transitions are allowed

	Can use energy levels to “fingerprint” elements and estimate temperatures.



Energy absorbed/emitted depends on upper and lower levels
Higher energy levels are close together
Above a certain energy, electron can escape (ionization)

Series of lines named for bottom level
	To get absorption, lower level must be occupied
		Depends upon temperature of atoms
	To get emission, upper level must be occupied
		Can get down-ward cascade through many levels